Particle methods for PDEs arising in financial modeling

[1]  Andrea Pascucci,et al.  Approximations for Asian Options in Local Volatility Models , 2011, J. Comput. Appl. Math..

[2]  Alexander Kurganov,et al.  A New Sticky Particle Method for Pressureless Gas Dynamics , 2007, SIAM J. Numer. Anal..

[3]  Alexander Kurganov,et al.  On a practical implementation of particle methods , 2006 .

[4]  Svante Janson,et al.  Feynman–kac Formulas for Black–Scholes–Type Operators , 2006 .

[5]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[6]  P. Schönbucher.  Credit Derivatives Pricing Models: Models, Pricing and Implementation , 2003 .

[7]  Alexander Lipton,et al.  Mathematical Methods for Foreign Exchange: A Financial Engineer's Approach , 2001 .

[8]  W. C. Schmid,et al.  Particle approximation of convection-diffusion equations , 2001 .

[9]  Michael Griebel,et al.  A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs , 2000, SIAM J. Sci. Comput..

[10]  H. O. Nordmark,et al.  Rezoning for higher order vortex methods , 1991 .

[11]  P. Degond,et al.  The weighted particle method for convection-diffusion equations , 1989 .

[12]  P. Degond,et al.  The weighted particle method for convection-diffusion equations. II. The anisotropic case , 1989 .

[13]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[14]  A. Leonard.  Vortex methods for flow simulation , 1980 .

[15]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[16]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[17]  A. Chorin.  Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.

[18]  G. Strang.  On the Construction and Comparison of Difference Schemes , 1968 .

[19]  H. Trotter.  On the product of semi-groups of operators , 1959 .

[20]  Francis H. Harlow,et al.  The Particle-In-Cell Method for Hydrodynamic Calculations , 1957 .

[21]  Kaitai Li,et al.  A third accurate operator splitting method , 2011, Math. Comput. Model..

[22]  Rogemar S. Mamon,et al.  Three ways to solve for bond prices in the Vasicek model , 2004, Adv. Decis. Sci..

[23]  J. Verwer,et al.  Numerical solution of time-dependent advection-diffusion-reaction equations , 2003 .

[24]  P. J. Schonbucher.  Credit Derivatives Pricing Models , 2003 .

[25]  P. Raviart.  An analysis of particle methods , 1985 .

[26]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[27]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .